Equivalence between representational similarity analysis, centered kernel alignment, and canonical correlations analysis

Centered kernel alignment (CKA) and representational similarity analysis (RSA) of dissimilarity matrices are two popular methods for quantifying similarity in neural representational geometry. Although they follow a conceptually similar approach, typical implementations of CKA and RSA tend to result in numerically different outcomes. Here, I show that these two approaches are largely equivalent once one incorporates a mean-centering step into RSA. This connection is quite simple to derive, but appears to have been thus far overlooked by the community studying neural representational geometry. By unifying these measures, this paper hopes to simplify a complex and fragmented literature on this subject.